The invention discloses a rapid-varying channel estimation method based on a low earth orbit satellite system. On the basis of relatively large Doppler frequency shift of a low earth orbit satellite and time frequency double-selection characteristics of a relay cascaded channel, a basis expansion model (BEM Basis Expansion Model) of a cascaded channel under an amplify forward (AF, Amplify Forward) protocol is established, and a channel estimation algorithm applicable to the BEM model is analyzed. The method comprises steps that firstly, according to normalized Doppler frequency offset and a signal to noise ratio, a to-be-selected BEM model is determined; and secondly, a least square algorithm (LS) and a linear minimum mean squared error (LMMSE) algorithm are selected through utilizing the channel sparse characteristics to estimate a model coefficient. According to the method, the basis expansion model can be utilized to reduce to-be-estimated parameters of a rapid-varying channel, in combination with the channel sparse characteristics and the adaptive hybrid BEM model, estimation precision is guaranteed while complexity of an elliptic basis function BEM (DPS-BEM) model and the LMMSE algorithm is reduced, and thereby efficient and accurate estimation is realized.